Rectangular Joint

Library

Joints

Description

This block represents a joint with two translational degrees
of freedom. Two prismatic primitives provide the two translational
degrees of freedom. The base and follower frames remain parallel during
simulation.

Joint Degrees of Freedom

The joint block represents motion between the base and follower
frames as a sequence of time-varying transformations. Each joint primitive
applies one transformation in this sequence. The transformation translates
or rotates the follower frame with respect to the joint primitive
base frame. For all but the first joint primitive, the base frame
coincides with the follower frame of the previous joint primitive
in the sequence.

At each time step during the simulation, the joint block applies
the sequence of time-varying frame transformations in this order:

Translation:

Along the X axis of the X Prismatic Primitive (Px)
base frame.

Along the Y axis of the Y Prismatic Primitive (Py)
base frame. This frame is coincident with the X Prismatic Primitive
(Px) follower frame.

The figure shows the sequence in which the joint transformations
occur at a given simulation time step. The resulting frame of each
transformation serves as the base frame for the following transformation.

Joint Transformation Sequence

A set of optional state targets guide assembly for each joint
primitive. Targets include position and velocity. A priority level
sets the relative importance of the state targets. If two targets
are incompatible, the priority level determines which of the targets
to satisfy.

Each joint primitive has a set of optional actuation and sensing
ports. Actuation ports accept physical signal inputs that drive the
joint primitives. These inputs can be forces and torques or a desired
joint trajectory. Sensing ports provide physical signal outputs that
measure joint primitive motion as well as actuation forces and torques.
Actuation modes and sensing types vary with joint primitive.

Dialog Box and Parameters

Expandable sections provide parameters and options for the different
joint primitives. These primitives are the basic elements of a joint
block. They can be of three types: Revolute, Prismatic, or Spherical.
Joint blocks can have all, some, or none of these joint primitives.
For example, the Weld joint block has none.

The expandable sections are hierarchical. The top level of an
expandable section identifies joint primitive type and axis, e.g., X
Prismatic Primitive (Px). Within a joint primitive section
are four parameter groups. These contain parameters and options for
a joint primitive's initial state, internal mechanics, actuation,
and sensing.

Prismatic Primitive: State Targets

Specify the prismatic primitive state targets and their priority
levels. A state target is the desired value for one of the joint state
parameters—position and velocity. The priority level is the
relative importance of a state target. It determines how precisely
the target must be met. Use the Model Report tool in Mechanics Explorer
to check the assembly status for each joint state target.

Specify Position Target

Select this option to specify the desired joint primitive position
at time zero. This is the relative position, measured along the joint
primitive axis, of the follower frame origin with respect to the base
frame origin. The specified target is resolved in the base frame.
Selecting this option exposes priority and value fields.

Specify Velocity Target

Select this option to specify the desired joint primitive velocity
at time zero. This is the relative velocity, measured along the joint
primitive axis, of the follower frame origin with respect to the base
frame origin. It is resolved in the base frame. Selecting this option
exposes priority and value fields.

Priority

Select state target priority. This is the importance level assigned
to the state target. If all state targets cannot be simultaneously
satisfied, the priority level determines which targets to satisfy
first and how closely to satisfy them. This option applies to both
position and velocity state targets.

Enter the spring equilibrium position. This is the distance
between base and follower frame origins at which the spring force
is zero. The default value is 0. Select or enter
a physical unit. The default is m.

Spring Stiffness

Enter the linear spring constant. This is the force required
to displace the joint primitive by a unit distance. The default is 0.
Select or enter a physical unit. The default is N/m.

Damping Coefficient

Enter the linear damping coefficient. This is the force required
to maintain a constant joint primitive velocity between base and follower
frames. The default is 0. Select or enter a physical
unit. The default is N/(m/s).

Prismatic Primitive: Actuation

Specify actuation options for the prismatic joint primitive.
Actuation modes include Force and Motion.
Selecting Provided by Input from the drop-down
list for an actuation mode adds the corresponding physical signal
port to the block. Use this port to specify the input signal. Actuation
signals are resolved in the base frame.

Force

Select an actuation force setting. The default setting is None.

Actuation Force Setting

Description

None

No actuation force.

Provided by Input

Actuation force from physical signal input. The signal provides
the force acting on the follower frame with respect to the base frame
along the joint primitive axis. An equal and opposite force acts on
the base frame.

Automatically computed

Actuation force from automatic calculation. SimMechanics™ computes
and applies the actuation force based on model dynamics.

Prismatic Primitive: Sensing

Select the variables to sense in the prismatic joint primitive.
Selecting a variable exposes a physical signal port that outputs the
measured quantity as a function of time. Each quantity is measured
for the follower frame with respect to the base frame. It is resolved
in the base frame. You can use the measurement signals for analysis
or as input in a control system.

Position

Select this option to sense the relative position of the follower
frame origin with respect to the base frame origin along the joint
primitive axis.

Velocity

Select this option to sense the relative velocity of the follower
frame origin with respect to the base frame origin along the joint
primitive axis.

Acceleration

Select this option to sense the relative acceleration of the
follower frame origin with respect to the base frame origin along
the joint primitive axis.

Actuator Force

Select this option to sense the actuation force acting on the
follower frame with respect to the base frame along the joint primitive
axis.

Composite Force/Torque Sensing

Select the composite, or joint-wide, forces and torques to sense.
These are forces and torques that act not at individual joint primitives
but at the whole joint. Options include constraint and total forces
and torques.

During simulation, the block computes the selected composite
forces and torques acting between the base and follower port frames.
It outputs these variables using physical signal output ports. Check
the port labels to identify the output variables at different ports.

Direction

Forces and torques acting at joints do so in pairs. Newton's
third law of motion requires that every action be accompanied by an
equal and opposite reaction. If the base frame of a joint exerts a
force or torque on the follower frame, then the follower frame must
exert an equal and opposite force or torque on the base frame.

Select whether to sense the composite forces and torques exerted
by the base frame on the follower frame or vice versa. The force and
torque vector components are positive if they point along the positive
X, Y, and Z axes of the selected resolution frame.

Resolution Frame

You can resolve a vector quantity into Cartesian components
in different frames. If the resolution frames have different orientations,
then the measured components are themselves different—even
though the vector quantity remains the same.

Select the frame in which to resolve the sensed force and torque
variables. Possible resolution frames include Base and Follower.
The block outputs the Cartesian components of the sensed force and
torque vectors as observed in this frame.

Constraint Force

Joint blocks with fewer than three translational degrees of
freedom forbid motion along one or more axes. For example, the Gimbal
Joint block forbids translation along all axes. To prevent translation
along an axis, a joint block applies a constraint force between its
base and follower port frames. Constraint forces are orthogonal to
joint translation axes and therefore do no work.

Select the check box to compute and output the 3-D constraint
force vector [fcx, fcy, fcz]
acting at the joint. Only constraint force components that are orthogonal
to the joint translational degrees of freedom have nonzero values.
Selecting this option causes the block to expose physical signal port
fc.

Constraint Torque

Joint blocks with fewer than three rotational degrees of freedom
forbid motion about one or more axes. For example, the Cartesian Joint
block forbids rotation about all axes. To prevent rotation about an
axis, a joint block applies a constraint torque between its base and
follower port frames. Constraint torques are orthogonal to joint rotation
axes and therefore do no work.

Select the check box to compute and output the 3-D constraint
torque vector [tcx, tcy, tcz]
acting at the joint. Only constraint torque components that are orthogonal
to the joint rotational degrees of freedom have nonzero values. Selecting
this option causes the block to expose physical signal port tc.

Total Force

A joint block generally applies various forces between its port
frames:

The net sum of the different force components equals
the total force acting between the joint port frames. Select the check
box to compute and output the 3-D total force vector [ftx, fty, ftz].
Selecting this option causes the block to expose physical signal port
ft.

Total Torque

A joint block generally applies various torques between its
port frames:

Constraint torques that forbid motion in directions
orthogonal to the revolute or spherical joint primitive axes.

The net sum of the different torque components equals the total
torque acting at a joint. Select the check box to compute and output
the 3-D total torque vector [ttx, tty, ttz].
Selecting this option causes the block to expose physical signal port
tt.

Ports

The block contains frame ports B and F, representing base and
follower frames, respectively. Selecting actuation or sensing options
from the dialog box exposes additional physical signal ports. Use
the ports to input an actuation signal or to output the chosen sensing
parameter.

A unique label identifies the actuation or sensing component
associated with a port. This label can contain one or two letters.
The first letter identifies the actuation or sensing parameter, applied
to or measured from the follower frame. The second letter identifies
the axis for that parameter, resolved in the base frame. This letter
can be x, y, or z.

The table describes the first letters in the port labels for
this block.